Two points were randomly thrown in the square.
Let's consider the circle which has these two points as ends of some diameter.
What is the probability this circle lies strictly inside the square ?

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Well, beyond my humble capabilities, but did you think of "getting in the mood"
by using something simpler, like a 4by4 checkerboard square with it's 9 points inside?

2 of the 9 points are picked at random, distance between the 2 points being the diameter.
Here we know that 5 diameter lengths are possible: 1, 2, sqrt(2), sqrt(5) and sqrt(.
Solve that...then graduate...